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Rectilinear propagation of light

Chapter: Optics

Question 1 of 5 NDA MCQ

Light of uniform intensity impinges perpendicularly on a totally reflecting surface. If the area of the surface is halved, the radiation force on it will become

Detailed Explanation

Correct Answer

✓ Option (b) is correct. The radiation force on the surface decreases when the area is halved.

📖 Governing Law / Core Concept

The governing principle is the concept of radiation pressure, which is given by the equation: \[ F = \frac{I \cdot A}{c} \] where: - \( F \) = force (N) - \( I \) = intensity of the radiation (W/m²) - \( A \) = area of the surface (m²) - \( c \) = speed of light in vacuum (\(3 \times 10^8\) m/s)

🧪 Step-by-Step Breakdown

For a surface area \( A \), the force due to radiation is: \[ F_1 = \frac{I \cdot A}{c} \] If the area is halved, i.e., \( A' = \frac{A}{2} \), then the new force \( F_2 \) becomes: \[ F_2 = \frac{I \cdot A'}{c} = \frac{I \cdot \frac{A}{2}}{c} = \frac{1}{2} \frac{I \cdot A}{c} = \frac{1}{2} F_1 \] Thus, the radiation force on the surface is halved.

🔍 Option Analysis

- **Option (a)**: Double – Incorrect, as halving the area reduces the force. - **Option (c)**: Four times – Incorrect, no square relationship with area. - **Option (d)**: One fourth – Incorrect, area reduction does not yield this result.

⚡ Mnemonic / Speed-Run

Recall that intensity and area directly affect force: **Area down, force down**.

6. Visual Suggestion

6. Visual Suggestion

A schematic showing a beam of light striking a surface, with area indicators before and after, clearly illustrating the reduction in area and its effect on radiation force.

📖 Factual Verification & Reference

📖 Factual Verification & Reference:

Verified against NCERT Class XII Physics, Chapter on Wave Optics.

Question 2 of 5 NDA MCQ

The streaming of light beams coming from the Sun through trees is said to have suggested that light travels in straight line. The particles on the path of light beams are visible to us because

Detailed Explanation

Explanation: The dust particle on the path of light is visible because of scattering of light.

Question 3 of 5 NDA MCQ

If the speed of light in carbon disulphide and vacuum is X and Y, respectively, then

Detailed Explanation
✓

1. Correct Answer

Option A is correct. The speed of light in carbon disulphide is less than in a vacuum.

📖 Core Concept

The speed of light is the fastest in a vacuum and decreases when traveling through other media such as carbon disulphide.

💡 3. Explanation

The speed of light \( c \) in any medium is defined by the equation:
\[ c = \frac{c_0}{n} \]
where \( c_0 \) is the speed of light in vacuum (approximately \( 299,792,458 \, \text{m/s} \)) and \( n \) is the refractive index of the medium. The refractive index \( n \) of all media other than a vacuum is greater than 1, meaning:
\[ c < c_0 \]
Consequently, the speed of light in carbon disulphide \( X \) is less than that in a vacuum \( Y \), thus confirming that \( X < Y \).

❌ 4. Option Analysis

  • • Option B: Incorrect because light slows down in any medium rather than speeding up.
  • • Option C: Incorrect as it suggests speed in a medium could be equal to or exceed that in a vacuum, violating light speed principles.
  • • Option D: Incorrect because speeds in mediums can never reach the speed in a vacuum.
⚡

NDA Speed-Run / Mnemonic Shortcut

Remember: "Vacuum for Velocity" - Light speed is always fastest in a vacuum compared to any other medium!

🎯

5. Key Takeaways

The speed of light in any medium is always less than in a vacuum due to the refractive index being greater than one.

Question 4 of 5 NDA MCQ

Consider the following statements about Light year:

(1) Light year is a unit for measurement of very large distances.

(2) Light year is a unit for measurement of very large time intervals.

 (3) Light year is a unit for measurement of intensity of light.

Which of the statements given above is/are correct?

Detailed Explanation

Correct Answer

✓ Option (d) is correct. Light year is exclusively a unit for measuring distances.

📖 Core Concept

Light year is defined as the distance that light travels in a vacuum in one year, approximately \( 9.46 \times 10^{12} \) kilometers.

🧪 Step-by-Step Breakdown

The key points regarding the statements are:
\[ \text{Distance (d)} = \text{Speed of light (c)} \times \text{Time (t)} \]
where: - \( c \approx 3.00 \times 10^8 \, \text{m/s} \) - \( t = 1 \, \text{year} = 365.25 \times 24 \times 60 \times 60 \, \text{s} \) Thus, the total distance \( d \) in a light year can be calculated as: \[ d = 3.00 \times 10^8 \, \text{m/s} \times (365.25 \times 24 \times 60 \times 60) \, \text{s} \]

🔍 Option Analysis

- Statement (1): Correct, as light year measures vast distances in astronomy. - Statement (2): Incorrect, it does not measure time intervals. - Statement (3): Incorrect, as it is not a measure of light intensity.

⚡ Mnemonic / Speed-Run

Remember: **Light Year = Distance** traveled by light in one year.

6. Visual Suggestion

6. Visual Suggestion

A diagram can depict the distance light travels in one year, illustrating a straight line from point A to point B, representing 1 light year (approximately 9.46 trillion km).

📖 Factual Verification & Reference

📖 Factual Verification & Reference:

Verified against NCERT Class XII Physics, Chapter on Wave Optics.

Question 5 of 5 NDA MCQ

Which one of the following statements is not correct for light rays?

Detailed Explanation

Correct Answer

✓ Option (c) is correct. Light speeds up as it leaves a denser medium like water and enters a less dense medium like air.

📖 Governing Law / Core Concept

The speed of light (\( c \)) in different media is governed by Snell's Law and the principle of optical density. The speed can be described by the relation:

\[ c = \frac{c_0}{n} \]

where \( c_0 \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) m/s), and \( n \) is the refractive index of the medium.

🧪 Step-by-Step Breakdown

In water, the refractive index \( n \) is greater than that of air. Therefore:

\[ n_{\text{water}} > n_{\text{air}} \Rightarrow c_{\text{water}} < c_{\text{air}} \]

When light exits water (more dense) to air (less dense):

\[ c_{\text{air}} > c_{\text{water}} \]

🔍 Option Analysis

Option A: True; light travels at different speeds based on the medium. Option B: True; speed is approximately 300 million m/s in air. Option D: True; light does speed up when transitioning from glass to air.

⚡ Mnemonic / Speed-Run

Remember: "Light likes less density" – it speeds up when moving to a medium with lower optical density.

📊 Visual Suggestion

Visual Suggestion

Illustrate a ray diagram showing light transitioning from water to air, highlighting the change in speed and direction with labeled angles.

📖 Factual Verification & Reference

📖 Factual Verification & Reference:

Verified against NCERT Class XII Physics, Chapter on Optics.

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